Multi/many-objective evolutionary algorithm assisted by radial basis function models for expensive optimization

In this paper, a multi/many-objective optimization algorithm assisted by radial basis function is proposed based on reference vectors to solve computationally expensive optimization. According to the iteration, a set of candidates are first determined by the reference vectors guided evolutionary algorithm in a sub-cycle. Based on the candidate pool, a refinement regeneration strategy and a dynamic exploration strategy are required. The refinement regeneration strategy is adopted to update the reference vectors derived from three types of reference vectors (i.e., the coarse reference vectors, the random reference vectors, and the refined reference vectors). The dynamic exploration strategy aims to determine the infilling samples from the candidate pool, considering space-infilling characteristics in the design space and convergence in the objective space. By repeatedly selecting candidates, the refinement regeneration strategy, as well as the dynamic exploration strategy, the final Pareto-optimal solutions can be yielded when the termination condition is satisfied. To verify the effectiveness of the proposed algorithm in addressing low/high-dimensional multi/many-objective optimization, the algorithm is compared with three state-of-the-art surrogate-assisted evolutionary algorithms in terms of numerous benchmark problems and an engineering problem. According to the corresponding results, the competitiveness of the proposed algorithm is verified.